Equirectangular world-map UV layout - the sequel
Since you say you don't require any texturing, I've tried to accomplish what you want without any UV unwrapping, and I think I've got it working.  

Add a plane, tab into Edit mode, make sure everything is selected (it should be, but if it's not, hit A once or twice until it is), scale by 2 on the X axis and add a loop cut like this (CtrlR, place the mouse near one of the longer edges, left click to make the cut, then right click to release without moving the newly created edge).
  

Select everything (A twice) and make some subdivisions (W > S). If you have the tool shelf visible, the settings for the subdivisions should be available at the bottom of it, otherwise hit T to show it, or F6 to open a dialogue with those settings.
  

Extrude the continents. Since you explained your own method of doing this quite well in this question, I'm not going to go into details about that. What I've done here is simply selecting some vertices by dragging the circle select tool around randomly, then extruding.
  

Make sure the bottom vertices of the continents are selected. With the way I extruded the continents, I simply hit CtrlNumpad +, but with your method, you may need some more elaborate way.
  

Select also the rim of the plane.
If none of the currently selected vertices are on the rim, hold Shift while selecting one corner vertex, then hold Ctrl while selecting the other three corners, then finally click the first corner again while still holding Ctrl.
If some of the currently selected vertices are on the rim, hold Shift while selecting a currently unselected vertex on the rim, which is next to a selected one, also on the rim, then, while holding Ctrl, select another vertex on the rim, next to a selected one, also on the rim, and make sure the distance between the last selected one and the one you're about to select is covered by a straight line of only unselected vertices. If the distance between them passes a corner, first select that corner vertex while holding Ctrl.
  

Invert the selection (CtrlI) and delete the vertices that are now selected (X > V).
  

Switch to face select mode (CtrlTabNumpad 3). Now you need to select all the faces that are connected to the rim of the plane. Select a face at one end of a continous string of faces, then, while holding Ctrl, select the face at the other end of the same string of faces. While holding Shift, select a face at one end of another string of faces, then, while holding Ctrl, select the face at the other end of the same string of faces. Repeat this until all the faces that are connected to the rim of the plane are selected.
  

Delete the faces that you just selected (X > F).
  

Zoom in and pan around to see if there are any edges like in the image below. If there are, switch to edge select mode (CtrlTabNumpad 2), select and delete them (X > E).


Tab back to object mode. Add another plane and repeat steps 1 and 2 above on the new plane, possibly with fewer subdivisions if you so desire. This plane will be the ocean. In the following I will refer to the first plane as "the continents" and the second plane as "the ocean".  

If you do require UV unwrapping, now is the time to do it. In that case, tab into Edit mode, select the vertices highlighted in the image (make sure the corner vertices are not selected), add them to a new vertex group (CtrlG > A) and mark them as seam (CtrlE > A). Do this for both the planes before unwrapping.


Add an empty and set its rotation to -90° on both the X and Z axes. Select both planes (select one, then hold Shift while selecting the other). Add a Simple Deform modifier, set it to Bend, set the Origin to the empty and the angle to 180°. This will add the modifier only to the last selected of the planes, so move the mouse to the 3D view and hit CtrlL > I to copy the modifier to the other plane. Apply the modifier to both planes. A workaround to apply modifiers to several objects at once, is to press AltC > M with all objects selected.
  

Change the rotation of the empty to 0° on the Z axis (but keep it to -90° on the X axis). Once again select both planes and add a Simple Deform modifier, set it to Bend, set origin to the empty and this time set the angle to 360°. Copy the modifier as above, and apply it to both planes as above. Now you can safely delete the empty if you wish.
  

The next step depends on whether you UV unwrapped or not.  

If you did not UV unwrap:
Select the ocean, tab into Edit mode, make sure everything is selected and remove doubles (CtrlV > D).
Tab back to Object mode and select the continents. Tab into Edit mode, make sure everything is selected and remove doubles (CtrlV > D). If you have any vertices and/or edges that aren't connected to any faces, select those and delete them.


If you did UV unwrap:
Select one of the planes and tab into Edit mode. Make sure everything is deselected (CtrlA to deselect if anything is selected). Go to the Object Data tab, select the group and click Select. Remove doubles. The group can now be deleted by clicking the - sign next to the vertex group list. Repeat this for the other plane. Then follow the steps to delete vertices and/or edges that aren't connected to any faces as explained above under "If you did not UV unwrap.

If you simply select everything and remove doubles after UV unwrapping, the UV map will look like this.

If you follow the steps above, the UV map will look like this.


Tab back to Object mode and select the ocean. Set the origin to geometry (Object > Transform > Origin to Geometry).Scale it up slightly, to make the continents slightly sunken into the ocean. Snap the cursor to selected (ShiftS > U). Select the continents and set origin to the 3D cursor (Object > Transform > Origin to 3D Cursor).
  

Hit Z to go into wireframe view mode. Add a bone (ShiftA > A > S). Tab into Edit mode and make sure the whole bone is selected. Rotate the bone to point roughly to the centre of one of the continents, and scale it down a little so it doesn't reach the surface. This will be the control bone for an entire continent. Extrude it a few times (with the bone selected hit E; you will need to select the first bone before every extrusion, or the extrusion will come out of the new bone). Point the extruded bones to the edge of the continent. These extruded bones will control the deformation as the continents collide. The more bones you add, the better control you will have. While still in Edit mode, add a control bone for another continent, and make some extrusions.  

Once you have all the bones, tab into Object mode and make the armature the parent of the continents. Select the continents, then hold Shift while selecting the armature. Hit CtrlP and select a suitable option from the drop down menu. I used "With Automatic Weights" in my example, but I strongly suggest you use "With Empty Groups" and manually weight paint. I'm not going to go into details about that, but basically you'll need the groups affected by the control bones for whole continents to have that continent all red, while the groups affected by the extruded bones should be red around the tip of the corresponding bone and fade to blue further away. There are several questions about weight painting here on Blender.SE that will most likely be helpful if you don't know how to do it. You may want to rename the bones before parenting, to make it easier to know which bones controls what.
  

Hit Z to go back to solid view.  

And the result:
  

At this point you can join the two objects into one. Make sure they do not have any UV maps and/or vertex groups with the same name. Rename the UV maps and/or vertex groups if necessary, but keep in mind that if you rename any vertex groups that are controlled by bones, you need to rename the corresponding bones as well. If the two objects have identically named UV maps and/or vertex groups, these will be merged into one map or group in the joined object. Once you made sure about this, select both objects in Object mode (first select one, then, while holding Shift, select the other one), then press CtrlJ. Don't use the Boolean modifier, as this is sure to mess up the rig.

I have two reasons for using a plane for the ocean, rather than adding a sphere directly. The planes are easily scalable to equal size, so no need to calculate the radius of a sphere, and they will have the same origin.  

Credit should go to @LeonCheung for this answer, which I used to create spheres from planes.